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3.6.1 General Formulation
The strong form of the virtual work statement is where Here, is the mixture domain (whose boundaries are defined on the solid), is the virtual solid velocity, is the virtual relative fluid velocity, and is the virtual energy density. The weak form of this statement may be written as the difference between external virtual work and internal virtual work , where and Here, is the solid traction, is the fluid viscous traction, and is the normal component of the relative fluid velocity on the boundary , whose outward unit normal is . In practice, both and should contribute negligibly to , but they cannot be set exactly to zero since we need some small elasticity to regularize the deforming mixture mesh.